The local roughness measured over windows of size \(l<L\)  also scales with the window size \(l\) , with a local exponent \(\alpha _{loc}\) . Equivalently, the height-difference correlation function, Eq. (REF ), scales as \(G_2 \sim |\vec{r}|^{\alpha _{loc}}\) . In general, \(\alpha _{loc}=\alpha \)  (e.g. in the KPZ equation for \(\nu \ne 0\)  [1]}). However, there are some kinetic roughening systems (e.g., the tensionless KPZ equation [2]}) in which the local and the global scalings of the roughness with the window size are different, i.e. \(\alpha _{loc}\ne \alpha \) . Such a behavior is called anomalous scaling or anomalous kinetic roughening [3]}, [4]}, [5]}. The structure factor scales in this case as [6]}
\(S(\vec{k},t) \sim |\vec{k}|^{-(2\alpha + d)} f_{S} (|\vec{k}|^z t),\) 
